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IGST 2011

Exact solvability, or integrability for short, is normally a one or two dimensional blessing which sometimes occurs in condensed matter systems such as spin chains, the Hubbard model, some sigma models, etc. Recently it became clear that some four dimensional gauge theories are dual to two dimensional integrable sigma models and inherit their quantum integrability. This gives rise to outstanding opportunities for improving our understanding of nature at fundamental scales. For example, using integrability, the exact dimension of all operators in a four dimensional gauge theory are now conjectured. This is the first time ever that non-trivial (non-protected) quantities are computed at any value of the coupling in a strongly interacting field theory.

Progress in this field is still happening at an amazing pace. This includes, for example, using the Thermodynamic Bethe ansatz and the AdS/CFT Y-system for probing the finite size spectrum of the theory and computing four dimensional scattering amplitudes making use of integrability. The computations of higher point correlation functions are also starting to arise. At the same time mysterious connections between correlation functions in Liouville theory (an integrable theory) and the partition functions of certain N=2 Gauge theories have been found and wall crossing phenomena have been connected to thermodynamic Bethe ansatz equations.

The purpose of the IGST2011 conference is to assess the current status of this rapidly evolving field by bringing together experts in gauge theories, strings, integrable systems and mathematics. The conference will consist of 25 talks and will allow for plenty of time for discussions. Many of the speaking slots will be made apparent in the near future to allow for the latest developments.

The high-energy behavior of gauge theory amplitudes can be studied using the operator expansion in Wilson lines. I review the next-to-leading order calculations of the high-energy amplitudes in N=4 SYM and QCD.

Benjamin Basso, Princeton Centre for Theoretical Sciences

From Weak to Strong Coupling with GKP

Raphael Benichou, Vrije Universiteit Brussel

First-principles Derivation of the AdS/CFT Y- and T-systems

I will present a first-principles derivation of the AdS5/CFT4 T-system up to first non-trivial order in the large 't Hooft coupling expansion. The proof relies on the computation of quantum effects in the fusion of some special line operators, namely the transfer matrices. This computation is done in the pure spinor formalism for the superstring in AdS5xS5. I will also discuss the generalization of this computation to other integrable 2D CFTs that define string theory in AdS backgrounds

Simon Caron-Huot, Princeton University

Scattering Amplitudes from (super) Wilson Loops

The S-matrix of N=4 super Yang-Mills in the planar limit enjoys a remarkable duality with non-BPS null polygon Wilson loops in the same theory, but with the role of momenta and position interchanged. I will attempt to explain how such a duality works, by stressing how familiar notions such as factorization limits, unitarity and the loop integrand translate into simple and verifiable statements about Wilson loops. This requires a suitable supersymmetric extension of Wilson loops, which I will describe. I will then discuss recent progress in using the full supersymmetry of the theory on the Wilson loop side to simplify scattering amplitude computations.

Paul Fendley, University of Virginia

Edge Modes, Zero Modes and Conserved Charges in Parafermion Chains

Sergey Frolov, Trinity College, Dublin

Mirror TBA

The TBA approach to the AdS/CFT spectral problem is used to compute scaling dimensions of several operators dual to two-particle states of the l.c. AdS5 x S5 string theory. The implementation of the psu(2,2|4) symmetry in the TBA framework is discussed.

Nikolay Gromov, King's College

Quasiclassical 3pt Functions

We compute three-point functions of single trace operators in planar N = 4 SYM. We consider the limit where one of the operators is much smaller than the other two. We find a precise match between weak and strong coupling in the Frolov-Tseytlin classical limit for a very general class of classical solutions. To achieve this match we clarify the issue of back-reaction and identify precisely which three-point functions are captured by a classical computation.

Romuald Janik, Jagiellonian University

Towards 3-Point Correlation Functions of Heavy Operators

In this talk I will report on the computation at strong coupling of the AdS contribution to the 3-point correlation function of operators corresponding to classical strings which rotate in the S5. This contribution is universal for all operators which have only SO(6) charges.

Michio Jimbo, Rikkyo University

Fermionic Basis of Local Fields in the Sine-Gordon Model Michio Jimbo

In this talk we give a survey of recent developments concerning the fermionic structure in the sine-Gordon model. For the lattice counterpart (6 vertex model), we introduce fermions acting on the space of (quasi) local operators. The main theorem is a determinant formula for the expectation values of fermionic descendants of primary fields. In the continuum limit this construction gives rise to a basis of the space of all descendant fields, whose expectation values take a very simple form. Unexpectedly, it turns out that the action of our fermions on form factors coincides with yet another fermions which have been introduced some time ago by Babelon, Bernard and Smirnov.

We study the four-point correlation function of stress-tensor supermultiplets in N=4 SYM using the method of Lagrangian insertions. We argue that, as a corollary of N=4 superconformal symmetry, the resulting all-loop integrand possesses an unexpected complete symmetry under the exchange of the four external and all the internal (integration) points. This alone allows us to predict the integrand of the three-loop correlation function up to four undetermined constants. Further, exploiting the conjectured amplitude/correlation function duality, we are able to fully determine the three-loop integrand in the planar limit. We perform an independent check of this result by verifying that it is consistent with the operator product expansion, in particular that it correctly reproduces the three-loop anomalous dimension of the Konishi operator. As a byproduct of our study, we also obtain the three-point function of two half-BPS operators and one Konishi operator at three-loop level. We use the same technique to work out a compact form for the four-loop four-point integrand and discuss the generalisation to higher loops.

Martin Kruczenski, Purdue University

Euclidean Wilson Loops and Riemann Theta Functions

For N=4 super Yang-Mills theory, in the large-N limit and at strong coupling, Wilson loops can be computed using the AdS/CFT correspondence. In the case of flat Euclidean loops the dual computation consists in finding minimal area surfaces in Euclidean AdS3 space. In such case very few solutions were known. In this talk I will describe an infinite parameter family of minimal area surfaces that can be described analytically using Riemann Theta functions. Furthermore, for each Wilson loop a one parameter family of deformations that preserve the area can be exhibited explicitly. The area is given by a one dimensional integral over the world-sheet boundary.

Andre LeClair, Cornell University

On the Ratio of the Viscosity to Entropy Density for Quantum Gases in the Unitary Limit

In the so-called unitary limit of quantum gases, the scattering length diverges and the theory becomes scale invariant with dynamical exponent z=2. This point occurs precisely at the crossover between strongly coupled BEC and BCS. These systems are currently under intense experimental study using cold atoms and Feshbach resonances to tune the scattering length. We developed a new approach to the statistical mechanics of gases in higher dimensions modeled after the thermodynamic Bethe ansatz, i.e. based on the exact 2-body S-matrix. Calculations of the critical temperature Tc/T_F = 0.1 are in good agreement with experiments and Monte-Carlo studies. We also calculated the ratio of viscosity to entropy density and obtained 4.7 times the conjectured lower bound of 1/4 pi, in good agreement with very recent experiments. We also present evidence for a strongly interacting version of BEC.

Sergei Lukyanov, Rutgers University

Critical Values of the Yang-Yang Functional in the Quantum Sine-Gordon Model

Joseph Minahan, Uppsala University

New Applications for Supergraphs

J. Luis Miramontes, Universidad de Santiago de Compostela

A Relativistic Relative of GS Superstrings on AdS5 x S5

The motion of superstrings on symmetric space target spaces is classically equivalent, via the Pohlmeyer reduction, to a family of 2-d relativistic integrable field theories known as semisymmetric space sine-Gordon (SSSSG) theories. In this talk I will review recent progress in constructing the relativistic S-matrix corresponding to the quantum solution of the AdS5 x S5 SSSSG theory.

Jan Plefka, Humboldt University

Scattering Amplitudes and AdS/CFT Integrability

I will give a brief review on the subject of scattering amplitudes in N=4 super Yang-Mills focussing on their infinite dimensional symmetry structure at tree-level and the fate of these symmetries at loop-level in particular employing a Highs-Regulator for the IR divergencies.

Amit Sever, Perimeter Institute

Flux tubes, Integrability and the S-matrix of N=4 SYM

An object which has been under attack from several fronts is the planar S-matrix of N=4 SYM. One approach towards addressing the computation of scattering amplitudes using integrability is by using an analogues of an Operator Product Expansion for these observables. It is a very general expansion that is based on the dual conformal symmetry of the amplitudes or their dual description in terms of null polygon Wilson loops. In this expansion the Wilson loop/amplitude

is viewed as a transition amplitude for flux tube excitations. The flux tube in question is the color flux stretched between two fast moving quarks and the excitation are the excitations of that color flux. In the planar limit, it has an holographic description in terms of a two dimensional world sheet, known as the GKP string. For N=4 SYM, the dynamics of the flux excitation is integrable to all loops.

David Simmons-Duffin, Harvard University

N=1 SQCD and the Transverse Field Ising Model

We study the dimensions of non-chiral operators in the Veneziano limit of N=1 supersymmetric QCD in the conformal window. We show that when acting on gauge-invariant operators built out of scalars, the 1-loop dilatation operator is equivalent to the spin chain Hamiltonian of the 1D Ising model in a transverse magnetic field, which is a nontrivial integrable system that is exactly solvable at finite length. Solutions with periodic boundary conditions give the anomalous dimensions of flavor-singlet operators and solutions with fixed boundary conditions give the anomalous dimensions of operators whose ends contain open flavor indices.

David Skinner, Perimeter Institute

Twistor Methods in N=4 SYM

I review how N=4 SYM can be reformulated as a theory on twistor space, and explain various calculations that have been performed there. In particular, twistors turn out to be a powerful tool for investigating the duality between scattering amplitudes and null polygonal Wilson Loops in the planar limit. The BCFW recursion relations are interpreted as the loop equations for a supersymmetric generalization of the Wilson Loop.

Arkady Tseytlin, Imperial College London

Aspects of Quantum Pohlmeyer Reduced Theory for AdS5 x S5 Superstring

We will discuss recent progress in computing quantum corrections to S-matrix and partition function of Pohlmeyer reduction for AdS5 x S5 superstring theory.

Dmytro Volin, Pennsylvania State University

Defining the AdS/CFT Y-system and Solving it Using a Finite Set of Equations

I will show how to solve the AdS/CFT Y-system in terms of a finite set of nonlinear integral equations (FiNLIE). To uniquely define the solution we impose the set of constraints on the Y- and T-functions which can be summarized as: symmetry (PSU(2,2|4) + Z_4) + analyticity + large volume asymptotics. Some of these constraints describe previously unknown properties of the Y-system. As an important check of our approach, we showed that the proposed constraints can be also used to derive the infinite set of the TBA equations. We also successfully checked FiNLIE numerically for the case of Konishi operator.